migration of heaw elements ih grouni) water

WWRC-84-05

MIGRATION OF HEAW ELEMENTS IH GROUNI) WATER

FOLLOWING UBlPNIUM SOLUTION MINING OPERATIONS

Michael J. Humenick Randall J. Charbeneau Brian Hassler September 15, 1984

Department of Civil Engineering College of Engineering University of Wyoming

Research Project Technical Completion Report '(USGS G-879, Project No.05)

Prepared for: U.S. Department of the Interior

U.S. Geological Survey

The research on which this report is based was financed in part by the United States Department of the Interior as authorized by the Water Research and Development Act of 1978 (P.L. 95-467).

Contents of this publication do not necessarily reflect the views and policies of the United States Department of the Interior, nor does mention of trade names or commercial products contitute their endorsement by the U.S. Government.

Wyoming Water Research Center University of Wyoming

Laramie, Wyoming

1 ABSTRACT V

The attached report qresents simulation models and example output for the

analysis of heavy element migration in ground water from in-situ uranium

solution mining sites under conditions of ground water flow. The models are

one dimensional and include the effects of advection, dispersion, mass

transfer, and equilibrium for selected heavy elements. Previous laboratory

data for uranium, molybdenum, vanadium, selenium and arsenic were used to

obtain necessary mechanistic relationships used in the models. Hydrologic

characteristics and status of solution mining sites in Wyoming are

presented.

ii

TABLE OF CONTENTS

Chapter

1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 2 . CHARACTERISTICS OF WYOMING IN-SITU URANIUM

M I N I N G SITES . . . . . . . . . . . . . . . . . . . . . . Location and S ta tus of Mining S i t e s . . . . . . . . . Ground Water Restoration . . . . . . . . . . . . . . Detailed Summaries of Wyoming Mining S i t e s . . . . .

3. MASS TRANSFER AND EQUILIBRIUM OF HEAVY ELEMENTS 0

Surface Pa r t i t i on ing Model . . . . . . . . . . . . . Analysis of Recirculating Batch Reactor Data . . . . Determination of Mass Transfer Coeff ic ien ts . . . . .

4 . SIMULATIONMODEL . 0 s . a

Simulation Development . . . . . . . . . . . . . . . Discussion of Parameters Used During Simulation . . . . . . . . . . . . . . . . . . . . . Summary of Simulation Runs . . . . . . . . . . . . . Discussion of Simulation Runs . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . .

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . APPENDIX A . COMPUTER ALGORITHMS FOR MODELS A AND B . . . . . .

Page

1

2

2

6

10

25

25

29

33

37

37

41

43

56

58

60

61

iii

LIST OF FIGURES

Figure 1 . In-Situ Uranium Leaching S i t e s i n Wyoming . . . . . Figure 2 . Mass I n i t i a l vs . F i n a l L ix iv i en t Concentration.

Uranium and Molybdenum . . . . . . . . . . . . . . Figure 3 . Mass I n i t i a l vs . F i n a l L ix iv i en t Concentration.

Vanadium. Selenium. and Arsenic . . . . . . . . . . Figure 4 . Mass Transfer Coeff ic ien t f o r Uranium vs .

Super f i c i a l (Darcy) Veloci ty . . . . . . . . . . . Figure 5 . Mass Transfer Coef f i c i en t s f o r Selenium.

Molybdenum. and Arsenic . . . . . . . . . . . . . . Figure 6 . Output f o r Run 1 . Model A . . . . . . . . . . . . . Figure 7 . Output f o r Run 2 . Model A . . . . . . . . . . . . . Figure 8 . Output f o r Run 3 . ModelA . . . . . . . . . . . . . Figure 9 . Output f o r Run 4 . Model A . . . . . . . . . . . . . Figure 10 . Output f o r Run 5 . Model A . . . . . . . . . . . . . Figure 11 . Output f o r Run 6 . Model A . . . . . . . . . . . . . Figure 12 . Output f o r Run 1 . Model B . . . . . . . . . . . . . Figure 13 . Output f o r Run 2 . Model B . . . . . . . . . . . . . Figure 1 4 . Output f o r Run 3 . Model B . . . . . . . . . . . . . Figure 15 . Output f o r Run 4 . Model B . . . . . . . . . . . . . Figure 16 . Output f o r Run 5 . Model B . . . . . . . . . . . . . Figure 17 . Output f o r Run 6 . Model B . . . . . . . . . . . . .

Page

3

28

34

35

44

45

46

47

48

49

50

5 1

52

53

54

55

iv

LIST OF TABLES

TABLE I . IN-SITU MINING OPERATIONS I N WYOMING . . . . . . . . TABLE I1 . GROUND WATER QUALITY CLASSIFICATIONS . . . . . . . .

Page

5

7

V

CHAPTER 1

INTRODUCTION

The work reported herein is a continuation of research into the study of

migration of heavy elements from in-situ uranium solution mining sites

(Humenick, et ale, 1983). Initial work was performed in the laboratory to

determine the mechanism of heavy element release and to provide data which

could be used to develop simulation models for the transport and migration of

heavy elements from commercial mining sites under the influence of natural

ground water flow.

The objectives of this work were to develop simulation models based on

mass transfer and equilibrium data from the previous work and to evaluate the

importance of the parameters in the model in light of the extent of heavy

element migration. The migration results are based on hydrologic conditions

prevalent at commercial mining sites in Wyoming. Specific objectives were as

follows :

1. To develop a simulation model to predict the migration of heavy

elements (uranium, molybdenum, vanadium, selenium, and arsenic) under

conditions of one-dimensional transport in confined ground water aquifers that

have been subjected to uranium solution mining operations within and down dip

of the mining area;

2. to produce a model that will account for the processes of advection,

dispersion, and mass transfer within the ground water system;

3. to determine the significance of heavy element migration based on

model predictions for typical Wyoming mining sites.

CHAPTER 2

CHBBBCTERISTICS OF WYOMING IN-SITIJ URANIUM MINING SITES

To simulate actual mining sites in Wyoming, the permit files of the

Department of Environmental Quality (DEQ) were used to accumulate as much

hydrologic and geologic information as was available. Because of the

dispersed nature of the information, its accumulation and summary was an

important project task.

Location and Status of Mining Sites

The majority of uranium mining activity in Wyoming occurs in the

northeastern and south-central portion of the state. Johnson, Campbell,

Converse, and Fremont Counties have the greatest amount of activity at the

present time. The majority of solution mining efforts have taken place in

these areas, also (Figure 1).

At the present time, only one commercial uranium in-situ development

project is in operation in Wyoming. Sequoyah Fuels Corporation, a subsidiary

of Kerr McGee Nuclear Corporation, is the operator. The project involves the

Q Sand of the Fort Union formation in Converse County and is operated under a

research and development permit issued by the DEQ. Table I summarizes the

activity in Wyoming.

2

WYOMING

1

SHERIDAN M C-

CAYCULL 1 JOMNSON

013 I WASWAUIE I E molr

5' 5 '

7

CREYOWI NAlnONA 0

10 120 ?,2 w

I

w Am

4 r CARBON

,

I u i m

FIGURE 1. I n S i t u Uranium Leaching S i t e s i n Wyoming

Sites Shown in Figure 1

1. Arizona Public Services Co. Peterson Insitu Uranium Extraction Process

2. Uranium Resources Inc. North Platte Project

3. Cleveland Cliffs Iron Co, Collins Draw

4. Exxon Minerals CO. Highland Mine

5. Uranerz, USA, Inc. Ruth ISL Pilot Project

6. Sequoyah Fuels Corporation Q Sand Project

7. Sequoyah Fuels Corporation 0 Sand P r o j e c t

8. Wyoming Mineral Corporation Irigary Ranch

9. Ogle Petroleum Co, Bison Basin

10. Rocky Mountain Energy Nine Mile Lake

11. Western Nuclear - Christensen Ranch

12. Teton Exploration Drilling CO. Leuenberger Site

13. Rocky Mountain Energy Reno Ranch

4

TABLE I

Operator

Commercial Scale Exxon Minerals Co. Wyoming Mineral Corp. Rocky Mtn. Energy Ogle Petroleum Co.

Teton Exploration Drilling Co.

In-Situ Mining

Mine Name

Highland Mine Irigary Ranch Reno Ranch Bison Basin

Leuenburger

Research and Development Cleveland Cliffs Collins Draw Iron Co.

Operations in Wyoming

County

Converse Johnson Campbell Fremont

Converse

Formation

Fort Union Wasatch Wasatch Green River

Fort Union (Laney Member)

Camp b e 11 Wasatch

Kerr McGee Nuclear Kerr McGee Nuclear Kerr McGee Nuclear Uranerz, USA, Inc. Uranium Resources, Inc .

Arizona Public Services Co.

Bill Smith Project Converse Fort Union Q Sand Project Converse Fort Union Bill Smith Mine 6001 Converse Fort Union Ruth ISL Pilot Project Johnson Wasatch North Platte Project Converse Fort Union

Peterson In-Situ Converse Fort Union Uranium Extraction Process

Tfn Files (DEQ still analyzing data from these before issuing permanent permit)

Rocky Mtn. Energy Wyoming Mineral Co. Rocky Mtn. Energy Western Nuclear Kerr-McGee

Licenses to Explore Rocky Mtn. Energy Wyoming Mineral Co. Union Energy Mining Div.

Nuclear Dynamics Wold Nuclear Co. Texasgulf, Inc.

Nine Mile Lake Irigary Ranch Reno Ranch Christensen Ranch 0 Sand Project

Nine Mile Lake S-1-7 Pilot Test Battle Springs

Sundance Project Red Desert Radon Springs

Natrona Mesaverda Camp be 11 Wasatch Camp be 11 Wasatch

Wasatch Camp$11 Conve se Fort Union

Natrona Me saverda Johnson Sweetwater

Crook Sweetwater Fremont

5

Ground Water Restoration

Reclamation or ground water restoration involves meeting certain

contaminant criteria set by the DEQ and is based upon pre-existing conditions

before mining commences. The restoration goal of any permitted operation is

"background water quality." Background, as defined by DEQ, is "the

constituents or parameters and the concentrations or measurements which

describe water quality and water quality variability prior to subsurface

discharge." If background quality cannot be achieved for certain elements,

criteria are set for these constituents based on the present or potential

economic use of the water. The state of Wyoming classifies its ground waters

into four basic categories:

Class I. Suitable for domestic use. Class 11. Suitable for agricultural use. Class 111. Suitable for livestock. Class IV. Suitable for industry.

Established criteria for each of the first three classes are listed in Table

11. Additional criteria are outlined in DEQ's Water Quality Rules and

Regulations, Chapter VIII.

Several methods exist by which ground water restoration can be

obtained. They include: 1) Ground water sweep 2) Reverse osmosis 3) Electrodialysis 4 ) Anion/cation exchange.

Ground water sweep involves the direct removal of all contaminated waters

with no subsequent reinjection. Several pore volumes of water must be removed

from each pattern. In addition, pumps large enough to initiate effective

ground water sweep are often expensive.

6

UNDERGROUND WATER CLASS Use Suitability Constituent or Parameter

TABLE 11

GROUND WATER QUALITY CLASSIFICATIONS

I Domestic

Concentration*

Aluminum (Al) Ammonia Arsenic Barium (Ba) Beryllium (Be) Boron Cadmium (Cd) Chloride (Cl) Chromium (Cr) Cobalt (Co) Copper (Cu) Cyanide (CN) Fluoride(F) Hydrogen Sulfide

-0-

0.5l 0 -05 1.0

0.75 0 001

0.05

1.0 0.2

1.4-2.4 0.05

250.0

---

2

(H2S) Iron (Fe) 0.3

Lithium Manganese (Mn) 0.05

Nickel ---

Lead (Pb) 0 005 -0-

Mercury (Hg) 0 0002

Nitrate (N03-N) 10.0 Nitrite (N02-N) 1.0

(NO,+NO, )-N --- L Oil & Greasz

Phenol Selenium (Se ) Silver (Ag) Sulfate (SO ) Total Dissohed

Solids (TDS) Uranium (U) Vanadium (V) Zinc (Zn) PH SAR RSC Combined Total

3 Radium 226 and Radium 228

Virtually Free 0,001 0 001 0.05

250 .O 500.0

5 .O

5.0 6.5-9.0 S.U.

5pCi/l

I1 111 Agriculture Livestock

Concentration* Concentration*

5 .O

0.1

0.1 0.75 0 001

100.0 0.1 0.05 0.2

--0

ow-

ow-

--- 0--

5 .O 5 .O 2.5 0.2

0.2 --- --- --- --- lo 00 --- 0 002 ---

200 00 2000 . 0

5.0 0.1 2 00

4.5-9.0 S.U. 8 1.25 meq/l

5pci/1

--- lo 00 100.0 10.0 --- 0 005 ---

3000 .O 5000 . 0

5pCi/l

7

TABLE 11 (Cont'd.)

Total Strontium 90 8pCi/l Gross alpha particle radioactivity (in- cluding Radium 226 but excluding Radon and Urani~m)~ 15pCi/l

8pCi/l

15pCi/l

8pCi/l

*mg/l, unless otherwise indicated

'Total ammonia-ni t rogen.

'Dependent on the annual average of the maximum daily air temperature: 1.4 mg/l corresponds with a temperature range of 26.3 to 32.5 degrees C, and 2.4 mg/l corresponds with a temperature of 12.0 degrees C (53.7 degrees F) and below.

3Requirements and procedures for the measurement and analysis of gross alpha particle activity, Radium 226 and Radium 228 shall be the same as requirements and procedures of the U.S. Environmental Protection Agency, National Interim Primary Drinking Water Regulations, EPA-570/9-76-003, effective June 24, 1977.

8

Reverse osmosis is a process whereby pressure is applied to contaminated

water withdrawn from a well pattern across a permeable membrane. Most of the

water passes through the membrane, while most of the dissolved solids are

rejected by the membrane and concentrated. The purified waster is then

usually reinjected into the pattern. By reinjecting purified water into the

well system, any contaminants left behind by leaching are diluted. The

process continues until restoration is achieved.

Electrodialysis involves the use of semi-permeable membranes having anion

and cation exchange properties. The membranes are alternately stacked, and a

D.C. current is applied to them. In theory, the cation exchange membranes

allow only the passage of cations, and the anion exchange membranes allow only

the passage of anions. Therefore, with a number of alternating membranes set

up, the eventual cleanup of produced waters takes place. In practice, removal

of radiometrics is not always as complete as in reverse osmosis.

Additionally, power requirements for the equipment is extensive, and initial

capital outlay can be cost prohibitive and make the total project

uneconomical. Advantages include low pressure operating conditions, reduced

membrane fouling over reverse osmosis procedures, and lower chemical costs.

The anion/cation exchange units on the market incorporate resins which

selectively remove particular anions and cations from a flow stream. Their

drawbacks include the need to recharge or replace the resins after a certain

period of time, expense of spent regenerant disposal, and difficulty in

controlling the effluent quality of certain chemical species.

Full restoration of leached uranium sites is often dependent upon the

lixiviant used to recover the uranium and upon the baseline classification of

the water at the project outset. Problems have been most prevalent with

9

lixiviants containing ammonia. Ammonia has a high affinity for clay minerals

in the formation and is difficult to flush out over a short period of time.

The Cleveland Cliffs, Collins Draw, site is a case in point. The Wyoming DEQ

has deemed Cleveland Cliffs's restoration efforts at this site unsuccessful

due to ammonia contamination problems. No remedial action had been proposed

at the time of this report.

Total dissolved solids (TDS) remaining in leached sites have also

presented reclamation problems at several Wyoming leaching projects. It seems

that restoration efforts can bring TDS levels down to baseline contaminant

criteria; but after a period of time during which the site has been in a

stability mode and only monitored, the TDS level will rise above baseline

conditions at some sites. Such a rise may entail the need for further

restoration efforts and a reevaluation of past restoration activity by the

DEQ. The state currently requires a ground water stability mode of one year

during which time leached site characteristics are monitored, and no

restoration activity takes place.

Detailed Summaries of Wyoming Mining Sites

Information regarding the hydrologic and geologic character of the mining

sites in Wyoming is necessary input for simulation of ground water contaminant

migration from these sites. The following pages summarize important details

about these sites. These data have been obtained from the permit application

files of the DEQ.

One of the most important characteristics related to contaminant

migration is the ground water velocity under normal flow conditions for that

aquifer. The following pages show the range in velocity to be 1.23 ft/yr at

the Leuenburger site to 52 ft/yr at the Q Sand Project. These velocities are

10

superficial or Darcy velocities. Actual velocities are obtained by dividing

the Darcy velocity by the formation porosity.

11

Ogle Petroleum Co. Bison Basin Nine

Location Fremont Co. 50 miles southeast of Lander T27N R97W Sec. 25

Geoloqy

Format ion Green River

Average sand thickness 15 feet - ore 6.3 feet

- Average porosity 27%

Depth to formation 375 feet

Hydroloqic Characteristics

Average transmissivities ranged from 117 gpd/ft to 198 gpd/ft. The northern portion of the field had the greater transmissivity.

The average storage coefficient in the northern portion of the field was .000051. In the southern portion of the field storage coefficients ranged from .0000094 to .00017. A representative value of .000294 was calculated.

Hydraulic conductivity averaged 5.8 gpd/ft2.

A hydraulic gradient of .009 ft/ft yielded a reported groundwater velocity of 9 ft/yr in a southeast direction,

Activity

Currently ,no mining is taking place at the site. No restoration has been performed. The mine is currently on standby status with periodic withdrawals to maintain a cone of depression in the area, Mine owners are seeking a buyer for the property.

12

Teton Exploration Drilling Co. Leuenburger Site

Location Converse Go. 0 miles northeast of Glenrock T34N R74W

Geology

Format ion F o r t Union

Average sand thickness 50 feet


Depth to formation N sand 220 to 270 feet M sand 320 to 390 feet

Hydrologic Characteristics

N sand Average transmissivity = 700 gpd/ft,

Average storage coefficient = .000083.

Hydraulic conductivity = 14 gpd/ft2.

The groundwater velocity in the area is 2.5 ft/yr in a northeast direction.

M sand Transmissivities ranged from 260 gpd/ft to 410 gpd/ft. Average transmissivity = 320 gpd/ft.

The calculated storage coefficient ranged from .00026 to ,000065 and averaged ,00095.

Average hydraulic conductivity = 5.2 gpd/ft2.

The groundwater velocity in this sand is 1-23 ft/yr in a northeast direction.

Activity

Current operations are at a standstill. Teton

13

! I

Exploration and Drilling has completed reetoration

market conditions rebound, and DEQ gives its approval, ,commercial development could begin sometime in the future.

but DEQ has not yet given its final approval. If

Y

14

Rocky Mountain Energy Nine Mile Lake

Location Natrona Co. 12 miles north of Casper T35N R79W Secs. 27,34

P

Geoloqy

Format ion

Sand thickness

- Average porosity

Depth to formation

Mesaverda - Teapot Sandstone 30 to 80 feet

28%

500 feet


Transmissivities ranged from 1300 gpd/ft to 3800 gpd/ft with a consistent increase from the southeast to the northwest. The average transmissivity was 2800 gpd/ft.

The average storativity was reported as .000084.

An average hydraulic conductivity was calculated to be 35 gpd/ft2. * A hydraulic gradient in the area of 0.0034 indicated a groundwater flow velocity of 18 ft/yr in an east-southeast direction.

Activity

Data has been submitted to the Wyoming Department of Environmental Quality on the restoration of three sites on the property. A fourth site will be restored upon final approval of restoration activities at the other three sites.

* Calculated from available data.

15

Kerr McGee Nuclear (Sequoyia Fuels Corporation) Gl Sand Project

Location Converse Go. 20 miles north of Glenrock T36N R74W Sec. 36

-

Geology

Formation F o r t Union





Average transmissivity 780 gpd/ft

Average storativity 00018

Hydraulic conductivity 31 gpd/ft2.

Groundwater gradient is on the order of 50 ft/mile or 00095 ft/ft. This indicates a groundwater flow velocity on the order of 52 ft/yr *. Flow is generallyko the northeast.

Activity

Currently being mined.


16

Kerr McGee Nuclear (Sequoyia Fuels Corporation) 0 Sand Project

Location Converse Co. 20 miles north of Glenrock T36N R74W Sec. 36

Geoloqy

Formation

Sand thickness

. Average porosity

Depth to formation

Fort Union

300 feet-are 75 feet

27%

500 feet


Transmissivity = 7000 gpd/ft.

Storage coefficient = booo18b

Hydraulic conductivity = 28.6 gpd/ft2.

D i r e c t i o n of groundwater flow is S 3 5 E e velocity available.

Activity

No flow

Wyoming DEQ h a s not yet issued a permit to mine. Operations will begin upon issuance of permit.

17

Wyoming Mineral Carp. Irigary Ranch

Location Johnson Co. 50 miles southwest of Gillette T45N R77W Sec. 9

Geoloqy

Formation Upper Irigary Sandstone


- - Average porosity 23.4%

Depth to formation 100-150 feet

Hvdroloaic Characteristics

Transmissivities ranged from 373 gpdlft to 770 gpd/ft and averaged 501 gpd/ft.

Storage coefficients ranged from .00005 to .000026. Average storativity = .000023.

Hydraulic conductivity = 7.7 gpd/ft2, * A groundwater gradient of 0.009 ft/ft yielded a groundwater velocity of 13.7 ft/yr in a direction due west.

Activity

No mining activity has taken place for approximately two years. The mine is currently on standby status, Mining will continue sometime in the future,


18

Uranerz, U. 5. A. , Inc. Ruth ISL Pilot Project

Location Johnson Co. 10 miles east of Linch T42N R76-77W Secs. 13,14

Y

Geoloqy

Format ion Wasatch

Average sand thickness 90-100 feet

Average porosity 29%



Transmissivities ranged from 68.2 gpd/ft to 231 gpd/ft. Average transmissivity = 141.9 gpd/ft.

Storage coefficients ranged between .00001 and ,001. An average of .00063 was calculated from available data.

Hydraulic conductivity = 2.5 gpd/ft2.

Natural-groundwater flow in the area was reported as 2.5 ft/yr in a northwest direction.

Activity

Beginning restoration and reclamation activities are planned for the latter part of 1984. Additional plans have not been defined at present.

19

Cleveland Cliffs Iron Ccs. Collins Draw Site

Location Campbell Co. 13 miles northeast of Linch T43N R76W Secs. 35,36

Geology

Format ion Wasatch





Average transmissivity = 192 gpd/ft.


Average hydraulic conductivity = 3.7 g p d / f t 2 . K

A groundwater gradient of .008 ft/ft yielded a groundwater velocity of 6.3 ft/yr in a direction N19W.

Activity

Restoration activities continued through December 1982 at which time the mine was shut down into a groundwater stability mode. Wyoming DEQ has not given final approval of restoration. The company has no future plans for the mine.


20

Uranium Resources Inc. North Platte Project

Location Converse Co. 12 miles east of Glenrock T34N R73W Sec. 15

- Geoloqy

Format ion

Average sand thickness

Average porosity

Depth to formation

Fort Union

25 feet

27% (eetimated)

610 feet


Transrnis~rivities varied between 400 gpd/ft and 490 gpd/ft. Average transmissivity = 440 gpd/ft.

Calculated storage coefficient8 varied between .0000018 and .00015. Average storage coefficient = 0 00005.

Average hydraulic conductivity = 17.6 gpd/ft2.

No flow-velocities or hydraulic gradients reported.

Activity

Restoration considered complete February 1983.

Arizona Public Services Co. Peterson In Situ Uranium Extraction Processes

Location Converse Co. 12 miles east of Glenrock T34N R73W Secs. 26,35

- Geology

Formation Fort Union





Tranamissivities ranged from 242 gpd/ft to 372 gpd/ft. Mean transmissivity = 315 gpd/ft.

Storage coefficients ranged from .000018 to .00037 with an average value of .0001.

Hydraulic conductivity ranged from 5.4 g p d / f t 2 to 8.8 gpd/ft2. The average hydraulic c o n d u c t i y , r i t y w a s 7.7 gpd/f t2.

The hydraulic gradient in t h e area is . : 3 E i t / f t a n d yielded a groundwater velocity af L. '!4 L'c/yr .

Activity

Currently no mining is taking place.

22

..

Exxon Minerals CO.- Highland Mine

Location Converse CO. 16 miles NW of Douglas T36N R72W Secs. 21,24

Y

Geoloqy

Format ion Fort Union


Average porosity 29 7t



Transmissivities ranged from 259 gpd/ft to 517 gpd/ft. Average transmissivity = 382 gpdlft. Highest values of transmissivity were detected in the northeast portion of the site.

Storage coefficients ranged from .000018 to .000053. Average etorage coefficient = a000037.

Hydrauli-c conductivity averaged 16.6 gpd/ft2, * Based on a hydraulic gradient of .0047 ft/ft, a groundwater flow of 18 ft/yr w a 8 calculated.

Activity

Mine officials indicate that restoration is complete. No further operations at the site are anticipated for the future.


23

Western Nuclear - Christensen Ranch

Location Campbell Co. 50 miles southwest of Gillette T44N R76W Secs. 17,20

Geoloqy

Formation

Sqnd thickness

Average porosity

Depth to formation

Wasatch

up to 300 feet

30%

365 feet


Average transmissivity = 679 gpd/ft.


A hydraulic conductivity was calculated to be 2.3 gpd/f t2. * The groundwater velocity was Indicated as being 5 ft/yr in-. a direction N57W.

Activity

Currently a research and development permit is being sought for t h e property. If such a permit is approved by May, 1984 a pilot study will commence. Plans call for a second research and development site on t h e property lom me time in 1985.


24

CHAPTER 3

MASS TRANSFER AND EQUILIBEIrJH OF HEAVY ELEMENTS

Previous laboratory work performed at the University of Wyoming (1)

produced the basic mass transfer and equilibrium data used to analyze the

migration of heavy elements in ground water after solution mining had been

performed. An analysis of the data in Reference 1 using a simple mass

transport model produced a useful but somewhat unrealistic result which has

subsequently been improved. The data have been reanalyzed according to the

following surface partitioning model. The model is applied to the

recirculating batch reactor data described in Reference 1.

Surface Partitioning Model

The following is the nomenclature and dimensions for the parameters used

in the model.

Notation Dimensions

C

P

n

K

k

MO

%

Solution phase concentration

Solid phase concentration

Initial value of q

Bulk density

Porosity

Equilibrium distribution coef.

Mass transfer coef.

Mass of ore

Volume of voids (in column)

~

mg/a

mgla

mg/R

kg/R bulk

R voids/l bulk

dimensionless -1

day

R

25

Volume of reservoir & tubing after 'Ri a

ith sample

%i Volume of i sample R th

R Volume of fluid in apparatus after 'fi

'v + 'Ri ith sample =

ci Concentration in ith sample mg/a

qe, ce Equilibrium values as above

The equilibrium or partitioning between the bulk solution and solid

phases is given by

K = - e n c

which has units of mg "sorbed"/mg "solution." In this equation,values for

qe/ce were obtained from the equilibrium data from Reference 1 as shown in

Figures 2 and 3.

Equation 2 establishes continuity of mass for each heavy element at any

time t where the sum is taken over all samples taken from the batch reactors

up to time t .

Equation 3 is simply the volume continuity for each experiment.

= vv + QRo = TTv + TfRi + Tffo %i i ( 3 )

26

150

100

50

0

I

URAN I OM

I I

a 30

20

10

I I I 1 I I I

MOLYR@ENUM

0 10 20 30 40

FINAL L I X I V I E N T CONCENTRATION, mg/l 0 4 8 1 2

FINAL L I X I V I E N T CONCENTRATION, m q / l

FIG, 2, MASS I N I T I A L VS F INAL L I X I V I E N T CONCENTRATTQN, URANIIJY AND MOLYBDENUM

6

4

2

0 ,

v V I I I 1

VANADIUM

I I I I I I I 0 0.2 0.4 0.6

FINAL L I X I V I E N T CONCENTRATION, mg/l I I I I I I I

SELENIUM

e

. I b I n I

0 0.2 0.4 0.6

FINAL L I X I V I E N T CONCENTRATION, mg/l

I I v I

0 ARSENIC

0 0.1 0.2 0.3 0.4

FINAL L I X I V I E N T CONCENTRATION, mg/l

FIG. 3. MASS I N I T I A L VS FINAL L I X I V I E N T CflNCENTRATION. VANADIUM, SELENIUM, AND ARSENIC.

Here vf0 and VRo are the initial values for the volume of fluid in the

apparatus and reservoir.

Writing Eq. 2 for equilibrium conditions, results in e e r M o = q M + c

0

and combining Eq. 4 with Eq. 1 gives

1 r - - l?

i si Mo 1 nK vfi - + - D M

( 4 )

( 5 )

0

This result will be useful later when the data from the batch reactors are

analyzed. In general, for any time period between samples, Eq. 2 gives

.fi 1 = r - c--- ci Vsi

MO Mo i

Analysis of Recirculating Batch Reactor Data

The recirculating batch reactors were small columns (12.54 cm inside

diameter containing about 100 gms of ore) through which various fluids were

recirculated from a reservoir (see Reference 1 for details of experimental

apparatus). Samples of the fluids were withdrawn occasionally for heavy

element analysis until an equilibrium concentration was established in the

recirculating fluid. The purpose of these experiments was to determine the

rate of heavy element release to the recirculating fluid. The recirculating

fluid initially had the composition of a typical ground water at uranium

29

solution mining sites. Thus, the experiments simulated release of heavy

elements to ground water when normal ground water flow was reestablished at

these sites.

Because the rate of heavy element release to the recirculating fluid was

observed to be slow compared to the flow through velocity, it was assumed that

mixing (dispersion) within the column was insignificant. Thus, basic

equations for conservation of mass for the heavy elements were written as

follows . Solution phase:

Solid phase:

- - = dq k(c - -) pq n dt nK

The third term in Eq. 7 represents the advective transport due to flow-through

(seepage) velocity u. Again, because the kinetics of mass transfer was

observed to be very slow, it was assumed that at any time t , the bulk

solution concentration in and out of the column was very nearly the same.

Thus, dc/dx 0 and the term was neglected.

Equation 8 is the mass conservation equation for the solid phase, and c - pq/nK is the generalized driving force for mass release. (Note: at

equilibrium, this driving force vanishes.) Now, neglecting the advective term

in Eq. 7 and combining Eqs. 7 and 8, one finds

30

- + dc k[c - -1 P4 = 0 dt nK (9)

In the general case, this equation cannot be solved because both c and q

are functions of time. However, the experimental data can be used via Eq. 6

which relates c and q, so Eq. 9 may be written

- + dc k(l+-) PYfi c = - ( r k P - - nK nKM o dt

Now the forcing function (right-hand side) in Eq. 10 is a piecewise constant,

and the equation may be solved for time intervals between samples.

For simplicity, write Eq. 10 as

dc - + a c = b dt n n

where

Pffi a = k(1 + -) n nKM

0

Using initial conditions of c(t=O) = c , and defining gn as n-1

n-1

n- 1

31

The concentration, cn, at time t = At which is the time between samples

having concentrations of cn and c n

is n-1

For purposes of obtaining values of the mass transfer coefficient, k,

from the experimental data, Eq. 15 is solved for an and values of k determined

for various time intervals during each run.

'n-1 1 +

The values for k were then averaged for each run.

Because of the simple way gn enters Eq. 15, it was interesting to

evaluate its physical significance. Returning to the definition of gn (Eq.

14), the total mass of heavy element remaining in the system between time tn

and tn-l is

n-1

C T T - 1 i=1 i si Mo

nKM and fT is the corresponding fluid volume. The term - can be shown to

be equal to (qe/ce)Mo which has units of (volume of voids) (mass sorbed/mass fn-l P

solution). Therefore, /p is the hypothetical volume which would be 0

occupied by the mass of heavy element at equilibrium if it was in the solution

32

phase rather than the sorbed phase. Thus,

- mass remaining - gn actual fluid volume + hypothetical volume

and this represents a concentration which is a driving force for mass

transfer . Determination of Mass Transfer Coefficients

The previous section shows the development of the equations used to

determine values for the mass transfer coefficients. The basic idea was to

obtain the rate of heavy element release between sampling periods and average

the values obtained during each run. The results of these calculations

follow. All k values were for a temperature of approximately 21OC.

Uranium. Figure 4 shows the results of calculations for the mass

transfer coefficient for uranium. It was found that the ground water velocity

had some effect on the value for k. In Chapter 2, natural ground water flow

velocities were seen to be very l o w in typical uranium solution mining ore

bodies. These values were well below that which could be practically used in

the laboratory experiments. Thus, some adjustment of linear extrapolation to

the lowest values for k might be warranted.

The difficulty of extrapolation of data to actual ground water velocities

is shown in Figure 4. When simulations are carried out as described in

Chapter 4 , a range such as that shown in the figure may be used to find the

most conservative prediction by the appropriate computer code.

Molybdenum. Figure 5 shows a similar velocity response for molybdenum as

that for uranium. In this instance, the mass transfer coefficient is

proportional to the 0.29 power of the velocity.

33

F I

U 2

0.1 8

6 4

* 2 !E

E * 0.01

w w . P - o

8

6

4

2

0,001

1 1 1 . v 1 1 . . I 1 I . v 1 1 ?

URAN I UM

T Y P I C A L FLOW V E L O C I T I E S

.

z -

0 . 3 3 k = 0.014V

O F

4 6 8 1 0 2 4 6 8 100 0.01 2 4 6 8 0 . 1 2 4 6 8 1 . 0 2

V . S U P E R F I C I A L V E L O C I T Y . m/dav

F I G U R E 4 . MASS TRANSFER C O E F F I C I E N T FOR URANIUM VS S U P E R F I C I A L (DARCY) V E L O C I T Y 4

S€

k, M

ASS

TRAN

SFER

CO

EFFI

CIE

NT,

da

y’’

. 0

0

., .,

., .

., 0

0

0

0

0

0

00

.

3

h3

P

01

03

-

0,

.

c

4

v,

‘?

m

XI

0

O

m - 0

m

ZI

c)

7

0

;4

vt m r

m

z

n

c

13:

Y i

w

U

m z

c

x

Y C

I

c) .

OI

03

d

0

Iu 0

P 0

m 0

00 0

d

0

0

rv 0 0

I I

1 I

P\

0

P % ro

I

I

I

I

1

Il

l

Vanadium. Only one run was able to yield data for vanadium. Most runs

had such low concentrations of vanadium in the recirculating ground water that

the analytical results were questionable. The only value obtained was 0.034

day- at a superficial (Darcy) velocity of 28.4 m/day. To obtain values at 1

lower Darcy velocities, extrapolation similar t o uranium or molybdenum are

recommended.

Selenium. The velocity response for selenium was found to be non-

linear. However, Figure 5 shows the relationship obtained, and extrapolation

may be achieved on a slope similar to uranium and molybdenum.

Arsenic. Figure 5 also shows arsenic to fol low a similar pattern as

uranium and molybdenum in the range of experimental results. Again,

determination of values for low velocities will require extrapolation.

36

cHApTEB4

SIMaLATION MIDEL

In this chapter, two simulation models are developed to predict the

migration of heavy elements from a uranium solution mining zone under

conditions of ground water flow. The model thus simulates the transport of

residual heavy elements left behind in the mining zone after mining operations

havq ceased and normal conditions have returned to the aquifer. Both models

are one-dimensional transport models that account for advection, dispersion,

heavy element mass transfer, and sorption.

The two models differ as follows:

Model A: Mass transfer is two-directional (both to and from the solid

phase) throughout the simulated domain.

Model 8: Mass transfer occurs only within the mining zone and only from

the immobile phase to the mobile phase. Outside the mining zone,

heavy element migration is controlled only by advection and

dispersion.

Simulation Development

For both models, the fundamental continuity equations for the solution

and solid phase are, respectively:

Here the nomenclature is the same as that in Chapter 3 . Additional parameters

are x, the distance in the direction of one-dimensional ground water flow;

37

D, the coefficient of hydrodynamic dispersion; and

the x direction.

u, the seepage velocity in

For simplification, the following dimensionless variables are introduced:

- x x = - - t = - Vt , - D D = - . = - E L ; c - E = - kL n U L ’ UL ’

In terms of these new variables, Equations (1) and (2) become

Equations (3) and ( 4 ) are not solved directly. Instead, new variables are

defined as

In terms of these new variables, equations (3) and ( 4 ) become

aA ac - a2c + A =

at aH aH2 - + - - D- -

D-- - 0 a~ ac - a2c at aH a? - + - - -

Equations (5) and ( 6 ) are analyzed as follows:

(5)

For computational simplicity, an explicit finite difference solution algorithm

was used. With Upwind differencing was used to avoid numerical dispersion.

38

an explicit solution, there are a number of stability requirements.

associated with the decay term is guaranteed as follows:

Stability

Decay Term

In equation (5), AA is separated into two terms, Mdecay and

%ransport.

Considering just the decay terms,

and thus

- '*decay = At [exp(-cAt)-l] ( 7 )

Transport Term

For both Equations (5 ) and ( 6 ) , the change associated with transport

is (using upwind differencing)

2DAt At n DAt At n +-)c +(-y-+-)c DAt n

AG2 i+l Ag2 AX i Ax2 A; 1-1 - - - C - (-

n where the notation ci is the concentration at the ith node point at time

step n. Using Equations (7) and (8), the changes AA and AB during the time

step are found for each node point. These changes are related to the

original concentration variables by

39

n+l KAY’’ + Bi = n+l

i l + K C

= = n+l i C

Final Equations

n+l n+l K(Bi - Ai )

1 + K

Combining equations (7 ) through (lo), we obtain

- - - -Eat + n 25At At Re - -

n+l = DAt

i A? Ax2 A; 1 + K ci ci+l - (7 + - - C

-kAt - 1 - - DAt A’i n =n Ax2 AH - ( e l + K ci + (y- + -) c i-1

K + ewkAt -kAt =n+l - K ( l - e )‘:+[ 1 + K

- 1 + K C i

( 9 )

Equations (11) and (12) are used in the computer algorithms given in Appendix

A.

Boundarv Conditions

1. c(x = 0,t) = 0

n Set i=l in (11) and let co = 0

k(x=L,t) - 2. - 0 (N nodes) ax

n n N Set i = N in (11) and let cN+l = c

Stability Criteria

1. Ax > uAt (Courant condition) UAX - u2At

t 2. D = au > (Upwind Differencing)

40

1 K

(1+K) (g) (2aiuAt)-l Ln

K ( l+K) At 3 . k

a = dispersivity

u = seepage velocity

The third stability condition is empirical and is based upon keeping the

coefficient multiplying ci in Eq. 11 negative. All three criteria are

checked before a simulation.

n

Discussion of Parameters Used During Simulation

1.

2.

3 .

4 .

The distance simulated was 5000 ft using 100 cells (N = 100) and; thus,

the cells size Ax = 50 ft. The number of cells in the mine zone, NSTAR,

varied from 1 to 10. Note that the mining zone is within the distance

simulated, L, and that in the plotted concentration profiles the mining

zone starts at x = 0.

DELT (At) was adjusted for each run so that stability was maintained and

printing and plotting occurred at desired time intervals. NSTEP, NPRNT,

and NPLOT were adjusted accordingly.

The initial concentration in the mine zone, CINT, was chosen to be 20

mg/l. Since the equations are linear, any other choice would have simply

rescaled the concentrations. By plotting relative concentrations c/CINT

and r/K*CINT , the plots would look the same regardless of the value of CINT chosen. Note that i/K*CINT is the fraction of initial heavy element

remaining on the ore in the mining zone.

Reported superficial velocities, V, varied from 1 to 50 ft/yr. A typical

value of 10 ft/yr was chosen for these simulations. A value of V = 10

ft/yr corresponds to a seepage velocity of u = V/n = 30 ft/yr. With a

41

distance L = 5000 ft, this gives a flow thru time for the domain of L/u =

166.7 yrsm

5. A porosity of 0.3 was used for all runs (n =0.3).

6m The choice of an appropriate dispersivity a = DIS is uncertain. The

following model is usually used for the coefficient of hydrodynamic

dispersion.

d D = a u + D a = Dispersivity

Dd = Effective diffusion coefficient

The term a u represents the mixing associated with the complex structure

of the porous matrix. Typical values of dd generally vary from 0.005 to

0.25 ft /yr. When values of CL are measured in the laboratory for

uniform soils, a generally ranges from 0.1 to 10 mm. However, in the

field, the soils are not homogeneous, and much larger values are

reported; for example, 100 m and larger. Regardless, it is apparent that

the model used in the simulation code is

2

au >> Dd in the field, and D = au. Values of a of 10, 25, and 100 ft are used, which is expected

to be in the relevant range.

7 . The values of K(ZEQ) are obtained from Figures 2 and 3 . Simulations

shown are for uranium which has qe/ce = 3.1 mg/kg ore/mg/l. Using a bulk

density, p, of 1.9 gm/cm3 and a porosity of 0.3, K has a dimensionless

value of about 20. (EQ = 20).

8 . The mass transfer coefficient, k(rKIN), may be obtained from Figures 4

and 5. Because of the uncertainty in extrapolation of data to low

seepage velocities, a range of values were used in the simulations for

42

uranium to determine the sensitivity of this parameter to the

concentration profiles. Values for k used in the attached simulations

were varied between 0.023 yr to 7.0 yr . -1 -1

Summary of Simulation Runs

A number of preliminary computer runs were carried out to verify the

mathematical model, to show that it was working properly, to test the

stability criteria, and to examine model sensitivity to input parameter

values. These runs are not presented here.

The following runs provide the basis for discussion of results. For each

run, both models were simulated with the indicated values for listed

parameters. Plots of the computer outputs are shown in Figures 6 through 17.

Run 1

u = 30 ft/yr k = 0.023 yr-' L = 5000 ft Ax = 50 ft

Run 2

u = 30ft/yr k = 0.023 yr" L = 5000 ft Ax = 50 ft

K = 20.0 At = 1 yr a = 10 ft NSTAR = 4

K = 20 At = 0.25 yr

a = 100 ft NSTAR = 4

4 3

CONCE NTRAT I: ON PROF I: L E S

SOLUTION PHASE *

LOCUS OF PEAK CONCENTRATIONS * ?J *

?L

00 0: 20 0: 40 0 . 8 0 1.00 OIY DISTANCE X L

c M I N E ZONE

50 YRS SOLID PHASE

0 f

RUN PARAMETERS : u = 30 ft/yr k = 0.023 yr-'

500 YRS L = 5000 ft Ax = 50 ft

K = 20 At = 1 yr a = 10 ft NSTAR = 4

I I I I 00 0.20 0.40 0 . 8 0 1.00

DISTANCE

FIGURE 6 . OUTPUT FOR RUN 1 . MODEL A

44

CJ

0i

0 . 40 0; 80 -0.00 0 . 2 0

CONCENTRATION P R O F I L E S

1.00

SOLUTION PHASE

~ ~ 2 5 0 YRS RUN PARAMETERS : b N

0- u = 30 ft/yr

L = 5000 ft

(1

0 W k = 0.023 yr" * i 3 Ax = 50 ft

\" A t = 0.25 yr z

gs NSTAR = 4

K = 20 0 0'

4 a = 100 ft

0'

0 0

0 c

1 I I 1

0 . 0 0 0 . 2 0 0 . 40 0 . 6 9 0 . 8 0 1,

* LOCUS OF PEAK CONCENTRATIONS sl 0 0 n . I

0

0 F ' - M I N E ZONE F 1

SOLID PHASE TZ5 yRS

00 DISTANCE X/L

FIGURE 7 . OUTPUT FOR RUN 2 . MODEL A .

45

- .... ._._ . .. .

I

0 CONCENTRATION PROFILES 0 .. c

m h

0 ..

!iig H

\ 0

(J 0'

In CJ

0 ..

0 0

S O L U T I O N PHASE

r/ 50 YRS

LOCUS OF PEAK CONCENTRATIONS

0' 0 . 0 0 0 . 2 0 0 . 40 0; 6 0

DISTANCE X/L 0: 00

RUN PARAMETERS : u = 30 f t /yr

k = 0 .23 yr-'

L = 5000 ft

Ax = 50 ft

K = 20 A t = 1 yr

u = 10 ft NSTAR = 4

I

1.00

-0. 00 0 . 2 0 0.40 0: 80 1.00 DISTANCE X L O * Y

F I G U R E 8. OUTPUT FOR RUN 3 . MODEL A .

46

CONCENTRATION PROF ILE S

SOLUTION PHASE

I

00 0; 20 0; 40 0 . 8 0 1.00 DISTANCE X/L

I RUN PARAMETERS : u = 30 ft/yr I\ .I I A k = 7.0 yr-'

I IR L = 5000 ft Ax = 50 ft

h K = 20 At = 0.2 yr

NSTAR = 4 a = 25 ft

h

1 . 00 0 .80 O * 7 00 0 , 2 0 0.40

DISTANCE X L

FIGURE 9. OUTPUT FOR RUN 4 , MODEL A .

47

0- 0 .

250 0 YRS 0

0 I 1 I 0 , 00 0 * 2 0 0,40 0 * 8 0

0 0

1.00

CONCENTRATION PROF I L E S

SOLUTION PHASE * * * LOCUS OF PEAK CONCENTRATIONS *

DISTANCE X

SOLID PHASE 25 YRS I

250 YRS #

RUN PARAMETERS : u = 30 ft/yr k = 0.023 yr-'

. L = 5000 ft

AX = 50 ft

K = 20 A t = 1.0 yr a = 2 5 ft

NSTAR = 10

00

FIGURE 10. OUTPUT FOR RUN 5 , MODEL A .

48

SOLUTION PHASE

*

8

LOCUS OF PEAK CONCENTRATIONS ' J % *

0 0

0 0 . 0 0 0 . 2 0 0.40 0 .60 0 . 8 0 1.00

DISTANCE X/L

0 C b

I I 1 I

00 0 .20 0.40 0.80 1.00 O - 7 DISTANCE X L

FIGURE 11. OUTPUT FOR RUN 6 , MODEL A

49

CONCE NTRATI ON PROF I L E S

0.20 0.40 00 80 0 0.00

0 0

.a

r

1.00

n b

0'

n CI(

0'

0 0

0' C

0 0 '

8

8 SOLUTION PHASE 8 8 8 8 LOCUS OF PEAK-CONCENTRATIONS *

I I

00 ol20 Oi40 0: 80 1.00 Oi Y DISTANCE X L

S O L I D PHASE I50 YRS

RUN PARAMETERS : u = 30 f t / y r

k = 0,023 yr-' L = 5000 f t - 200 YRS Ax = 50 f t

K 20

A t = 1 yr 0 = 10 f t

NJTAR = 4

FIGURE 12 . OUTPUT FOR RUN 1 . MODEL B .

50

c

0 0

c

u, b

0 *.

0

0 0

( 0

CONCENTRATION PROF IL ES m

SOLUTION PHASE

* * * LOCUS OF PEAK CONCENTRATIONS

125 YRS

D ISTANCE X

25 YRS SOLID PHASE

RUN PARAMETERS : u = 30 ft/yr k = 0.023 yr-' L = 5000 f t

,250 YRS

A x = 50 ft K = 20

A t = 0.25 yr a = 100 ft NSTAR = 4

I

BOO

0: 20 0: 40 0 . a0 1.00 O, 7 00

DISTANCE X L

FIGURE 13. OUTPUT FOR RUN 2 , MODEL B .

51

z5

1 X 33NVlSIO 00'1 08 '0 d,-0 0) '0 02 '0 00 'Oo

3SVHd 0110s

StlA 00s

SdA

1 X 33NVlSIO OO'L 08 '0 49 '0 OP 90 02 '0 00

SNOIlVdlN33N03 1V3d do Sn301 )+: F 4

3SVHd NOIlnlOS

S3 11 AOtJd NO IlVtJlN33N03 c

CONCENTRAT I ON PROF I: L E S

t

. o o 00 O: 7 0: 20 0: 40

DISTANCE X L

S O L I D PHASE

*50 YRS RUN PARAMETERS : u = 30 f t /yr

k = 7.0 yr-’

L = 5000 ft Ax = 50 ft

K = 20

A t = 0.2 yr

NSTAR = 4

a = 25 ft

- 250 YRS

00 O: 7 0: 20 0: 40

DISTANCE X L 0: 80 1 00

FIGURE 1 5 . OUTPUT FOR RUN 4 , MODEL B,

53

0 0 .. - Y) C.c

0'

b 0 0' 3 \ 0

Y) c3 0

o 4

0 0

CONCENTRATION PROF I L E S

SOLUTION PHASE

0 . 8 0 Oi 7 00 0: 20 0; 40

DISTANCE X L 1.00

- 25 YRS S Q L I D PHASE

- 250 YRS RUN PARAMETERS : u = 30 ft/yr k = 0.023 yr-' L = 5000 ft

A x = 50 ft K = 20

A t = 1.0 yr

NSTAR = 10 a = 25 ft

I 1 I I

7 DISTANCE X L

FIGURE 16. OUTPUT FOR RUN 5 , MODEL 6 .

54

0 0 .* r

v) I\

0'

i z 0 0' \ 0

v) c3 0'

0 0

0' C

Q 0

CONCENTRATION PROFILES

SOLUTION PHASE

*

* 8

* 8 ?L

00 0: 20 0: 40 0: 60 0: 80 1.00 DISTANCE X/L

SOLID PHASE

RUN PARAMETERS : u = 30 ft/yr k = 0.023 yr'l L = 5000 ft

Ax = 50 ft K = 20

At = 1.0 yr a = 25 ft NSTAR = 1

1 1 I I

00 0 . 2 0 0.40 0.80 1. 00 O * 7 DISTANCE X L

FIGURE 17 . OUTPUT FOR RUN 6. MODEL B ,

55

Run 3

Run 5

u = 30 ft/yr k = 0.23 yr-' L = 5000 ft Ax = 50 ft

Run 4

u = 30 ft/yr k = 7.0 yr-I L = 5000 ft Ax = 50 ft

u = 30 ft/yr k = 0.023 yr'l L = 5000 ft Ax = 50 ft

K = 20 At = 1 yr a = 10 ft NSTAR = 4

K = 20 At = 0.2 yr a = 25 ft

NSTAR = 4

K = 20 At = 1.0 yr a = 25 ft

NSTAR = 10

Run 6

Same as Run 5, except NSTAR = 1.

Discussion of Simulation Runs

It is important to note from the dimensionless form of the equations that -

the simulation results depend on two variables, x = X/L and i = Vt/L, and on

three parameters:

In addition, we assume that K is fixed from the experimental data at K =

20. Again, with L and u fixed, we may vary the parameters 5 and k by varying a and k, respectively.

Comparison of runs 1 and 2 shows the influence of mixing (5) for fixed

kinetics (z). The decrease in maximum concentration is more evident for model

B than for model A; however, in both cases, the differences are significant.

56

It is noted that these results are conservative in that transverse dispersion

is neglected in a one-dimensional model.

Comparison of runs 1, 3 and 4 shows the influence of the mass transfer

coefficient (E). The most dramatic effect noted with model A was the

tremendous decrease in the rate of migration of the species between runs 1 and

3. It appears that for k 0.23 yr , the rate of migration approaches that -1

of the equilibrium theory: U - water

chemical 1 + K - U

species

and the effective rate of migration of the metals is u = 30/21 = 1.5 ft/yr.

Comparison of runs 3 and 4 shows that a further increase in k does not

significantly affect the rate of migration, but the maximum concentrations do

increase. (This is shown even though a is greater in 4 than in 3 . ) Run 4 ,

Model A, shows

'. Note that

as they would

only influence

that the conditions of equilibrium are satisfied for k = 7 yr-

the scaled solution and solid phase concentrations are the same

be for equilibrium. The same runs for model B show that the

of increasing k is to increase the maximum concentrations.

Finally, comparison of runs 1, 5 and 6 show the influence of the mining

zone size, all for a low k = 0.023 yr-? Especially for model B, but also for

Model A, an increase in size corresponds to an increase in maximum

concentration downstream from the mine. There is no influence on the rate of

migration, but since the water is in contact with the mine zone longer, more

mass is released, leading to higher concentrations.

It is apparent from the wiggles in the concentration plots that the

solutions are near instability. However, the wiggles are dampened, and the

solutions remain accurate (for runs 5 and 6 ) .

57

Conclusions

While these few simulation runs have hardly been exhaustive, they do lead

to a number of important conclusions.

1. The simpler model B shows an increase in maximum concentrations

downstream of the mining zone with increasing k and size of the mine

zone, and with decreasing dispersivity a. This model is probably not

very realistic in that there is no mechanism for restabilization of the

metal released from the mine zone. Considering the 100-200 yr. time

period for water to travel 1 mile, this seems unlikely, although

conservative answers are obtained. Hereafter, just Model A is

considered.

2. The dispersivity is an important parameter inversely related to the

maximum downstream concentrations. In reality, the effective value of

a probably increases with distance of migration from the mine, as a

greater range of hydraulic heterogeneities are encountered. a could

likely be less than 1 ft. in the immediate vicinity of the mine.

However, the range 10-100 ft. is probably representative for the region

and type of aquifers considered.

3. The value of k plays a dual role. As k increases from 0.023 to 0.23

yr-', the rate of migration is greatly influenced. Already at k = 0.23

yr-' the rate of migration approaches that of an equilibrium model with

retardation factor Rd = 1 + K = 21. Further increases in k do not

greatly affect the rate of migration, but they do result in an increase

in maximum observed concentration. For k = 7 yr , equilibrium between the mobile and immobile phases is rapidly approached (in hydrogeologic

time), and one might suggest a mathematical model as follows:

-1

58

c

R d = I + K

erf = error function

Co = initial temperature

D = a u

If the metal is reduced and stabilized according to a first order rate law,

with rate coefficient , then the equation above would be multiplied by

The model above implies chemical equilibrium between a mobile and

immobile phase, with decay (stabilization).

59

REFERENCES

1. Humenick, M. J., W. L. Dam, and J. I. Drever, "Heavy Element Release to

Ground Water at In-Situ Uranium Mining Sites: Phase I,*' Wyoming Water

Research Center Report A-037-WYO, prepared for the U.S. Department of the

Interior, University of Wyoming, Laramie, WY, August 31, 1983.

60

APPENDIX A

COMPUTER ALGORITIPMS FOR MODELS A AND B

61

MODEL A

PROGRAM TUOPOR(I~PUI.OUTPUT+TRPES=TNPUT +TAPE6=OUTPUTtPLOT) C

' C C C C C C C c c C c C C C C C c C C C C C

C C C C C C C C C C C C C c C C C C

I C

C ' C ' C

' C C C C

PROGRAN TOTOPOR: O N E - D I ? K N S I O N ~ t TRANSPORT OF A SOLUTE IN A DUAL POROSXTY tFLOUXNG AND STAGNANT PHASES) GROUNDUATER AQUXFER USING AN EXPLICIT F I N I T E DIFFERENCE SOLUTTON UTTH UPSTREAH DIFFERENCING AND TIME A V & R A 6 I H G FOR HASS TRANSFER

D E F I N I T I O N O F VARrAOLES

C I N T t3ELX DEtT DIS EQ KIN M RIPLCT NPRMT NSTAR NSTEP POR V

XNITXhL SOLUTE CORCENTRATXON CELL S I Z E SIZ€ OF T I W STEP KITSPER S I V I T Y PAR T X T l ON COEFFIC IEMT MASS TRANSFER COEFFTCI€NT RlUMRER O F CEELLS NUtWrR OF TIRC STEPS BETUECN PLOTTING OUTPUT NUMPtR O F T I R E STEPS RETUEEN P R I N T I N G OUTPUT NURBE'R OF C € C t S Tht lbUTTTAL C O N T A H I M C A T E D ZONE NURBE'R O F TIME STEPS ACTIVE POROSITY SEEFAG€ VELOCITY fPI IBQUTFER

MOTE: PASSIVE PHASE COMCENTRfiTTQN R€ASURED IN SAME UNITS AS SOLUTION PHRSE CONCENTRATIOkI TO 6ET UNITS O F RASS PER PIASS, RULTIPLY BY THE POROSITY AND D I V I D E BY THE BULK DENSITV

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CORPUTE F I N I T E DIFFERENCE COEFFICIENTS

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MODEL B

PROGRAR T Y O P G l ~ I M P U T , ~ U T P U T t T A P E S = ~ N P ~ ~ ~ T A P ~ 6 = O U T P ~ T ~ P ~ ~ T ) . c

C C PRO6iRAH TUUPOI: O N E - D I H E N S I O N A L TRANSPORT O F d SOLUTE IN A C DUAL P QROSITY CFLOUTNG AND STAGNANT PHASES) C GROUNDUATER AQUIFER USING AN E X P L I C I T F IN ITE C DIFFERENCE SOLUTION WT1.H UPSTREAM DIFFEREMCING C AND TIRE AVERAGING FOR MASS TRANSFER- TRANSFER C IS ONE DIRECTIONAL0 c C C C

- c C

C C Ctf,J) = CONCUUTRRTXWI XN JTH CELL FOR 1 ) SOLUTE AT c BEGTNNXN6 O f TXRF STEP c [ I = l ) t 3) SOL10 PHASE AT C BEGINNING OF TIR'E STEP ( 1 = 2 > y 3) SOLUTlE AT END C OF TIME STEP qT=3>t AND 4 1 SQLYD PHRSE AT €ND C OF TfPE STEF CT=4> C c C I N T = I N I T I A L SOtUTr CUNCEMTRATION c DF.tX = CELL S I Z E C DCLT = SXZF OF 1 X W STEP C 0 IS = DISPERSXVXTY C f : ca = PARTITXOM CO€FFICXEMT c K I N = PASS TRAMSF€R CGEFFXCTEM? C N = NUHBCR O F CELLS C MPLOT = NUBPE'R OF TIME STEPS BETMEEN PLOTTXHG OUTPUT C RPRNT = NUrtPER OF TIRE STEPS RETWEEN PRTNTING OUTPUT C NSTAR = NUIIBER O F CELLS IN INXTI&l CaNTb@IN-TED ZONE C MSTEP = NUR8ER O F TXRE STEPS c PQR = ACTIVE POROSITY c v = SEEPAGE VELUCXTY IN AQUIFER C c C NOTE: PASSIVE PHASE CONCENTRATIOrtl YEASURED fPi SARE UNITS AS

c PER RASSI MULTIPLY BY THE POROSITY AND DIVIDE BY c THE BULK DENSITY C c .

. c D E F I N I T I O N OF VARIARLES

C S O L U T ~ I PHCISE C a N c E N i R A T n w ; TO GET UNITS OF RASS

REAL K I N

I T C Y A X t X O O I DIRENSION CC4 .lOD 3 9XARRAY f 102 1 +EARRAY C102) SCARRAY C 1021 9CMA XC XU0 3 9

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REAO ( 5 ~ 5 ) N r NSTAR rNSTEP yNPRNT rNPLOT YRITE ( 6 9 s ) N ~ ~ S T A R ~ ~ S T E P , N P R ~ T I N P ~ O ~

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66

C

C c C C

C C C

INITIALIZE CONCENTRATIONS

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C

C C C C

C C c C. C

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COHPUTE FINITE DIFFERENCE COEFFICIENTS

67

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C C C C

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CQHPUTATION FOR FIRST CELL

0 0 ' 5 0 8J=2rR

CQHPUTATION F O R LAST CELL

COHYUTATXON F O R RhSS FLUX OUT

PRfNT RESULTS FOR TIRE STEP

68

C C

69

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